Quiz 3 Ch 5
If r+si is a solution to the equation ax2+bx +4 =y with s not = 0, express the coordinates of the vertex of
the parabola in terms of r and s. Show all steps.
Quiz 3 Ch 5
If r+si is a solution to the equation ax2+bx +4 =y with s not = 0, express the coordinates of the vertex of
the parabola in terms of r and s. Show all steps.
Solution
We know from the quadratic formula that r+si =
Separating into real and imaginary parts
or if you factor out i 𝑠 =
𝑟=
−𝑏+√𝑏2 −4𝑎𝑐
2𝑎
−𝑏
2𝑎
and 𝑠𝑖 =
−𝑏
2𝑎
𝑘=
2𝑎
√−𝑏2 +4𝑎𝑐
2𝑎
Looking at the quadratic equation in vertex form 𝑦 −
ℎ=
√𝑏2 −4𝑎𝑐
−𝑏2 +4𝑎𝑐
4𝑎
−𝑏2 +4𝑎𝑐
= 𝑎 (𝑥 +
𝑏
2𝑎
2
)
4𝑎
Since r is h, the x coordinate of the vertex is 𝑟 =
−𝑏
2𝑎
Comparing s and k, the y coordinate of the vertex yields 𝑠 =
√−𝑏2 +4𝑎𝑐
2𝑎
−𝑏2 +4𝑎𝑐
4𝑎
With some algebra 𝑎𝑠 2 =
−𝑏2 +4𝑎𝑐
4𝑎2
k=
so k=𝑎𝑠 2
Then the coordinates of the vertex in terms of r and s are (𝑟, 𝑎𝑠 2 )
Solution
We know from the quadratic formula that r+si =
Separating into real and imaginary parts
or if you factor out i 𝑠 =
𝑟=
−𝑏+√𝑏2 −4𝑎𝑐
−𝑏
2𝑎
2𝑎
and 𝑠𝑖 =
ℎ=
2𝑎
𝑘=
2𝑎
√−𝑏2 +4𝑎𝑐
2𝑎
Looking at the quadratic equation in vertex form 𝑦 −
−𝑏
√𝑏2 −4𝑎𝑐
−𝑏2 +4𝑎𝑐
−𝑏2 +4𝑎𝑐
4𝑎
= 𝑎 (𝑥 +
𝑏
2
)
2𝑎
4𝑎
Since r is h, the x coordinate of the vertex is 𝑟 =
−𝑏
2𝑎
Comparing s and k, the y coordinate of the vertex yields 𝑠 =
−𝑏2 +4𝑎𝑐
4𝑎
With some algebra 𝑎𝑠 2 =
−𝑏2 +4𝑎𝑐
4𝑎2
√−𝑏2 +4𝑎𝑐
2𝑎
so k=𝑎𝑠 2
Then the coordinates of the vertex in terms of r and s are (𝑟, 𝑎𝑠 2 )
k=